High-entropy high-hardness metal carbides discovered by entropy descriptors

High-entropy materials have attracted considerable interest due to the combination of useful properties and promising applications. Predicting their formation remains the major hindrance to the discovery of new systems. Here we propose a descriptor - entropy forming ability - for addressing synthesizability from first principles. The formalism, based on the energy distribution spectrum of randomized calculations, captures the accessibility of equally-sampled states near the ground state and quantifies configurational disorder capable of stabilizing high-entropy homogeneous phases. The methodology is applied to disordered refractory 5-metal carbides - promising candidates for high-hardness applications. The descriptor correctly predicts the ease with which compositions can be experimentally synthesized as rock-salt high-entropy homogeneous phases, validating the ansatz, and in some cases, going beyond intuition. Several of these materials exhibit hardness up to 50% higher than rule of mixtures estimations. The entropy descriptor method has the potential to accelerate the search for high-entropy systems by rationally combining first principles with experimental synthesis and characterization.Comment: 12 pages, 2 figure

First principles computational descriptor for entropy forming ability

Entropy stabilized materials [1], where the mixing of the components is driven by configurational entropy rather than formation enthalpy, are potential candidates for ultra-high temperature applications. The prediction of which compositions will form entropy stabilized materials is difficult since calculating the entropic contribution to the free energy from first principles is computationally expensive. Therefore, we have formulated a descriptor for the synthesizability of disordered materials based on the energy distribution of the thermodynamic density of states (TDOS) for an ensemble of ordered configurations generated using the AFLOW (Automatic FLOW) partial occupation (AFLOW-POCC) methodology [2,3] and calculated with DFT. This descriptor has been used to successfully predict which refractory metal carbide compositions can be experimentally synthesized as single-phase entropy stabilized materials [4]. This work is supported by the U.S. Office of Naval Research MURI program (grant No. N00014-15- 1-2863). [1] C. M. Rost, E. Sachet, T. Borman, A. Moballegh, E. C. Dickey, D. Hou, J. L. Jones, S. Curtarolo, and J.-P. Maria, Entropy Stabilized Oxides, Nat. Commun. 6, 8485 (2015). [2] S. Curtarolo, W. Setyawan, G. L. W. Hart, M. Jahnatek, R. V. Chepulskii, R. H. Taylor, S. Wang, J. Xue, K. Yang, O. Levy, M. J. Mehl, H. T. Stokes, D. O. Demchenko, and D. Morgan, AFLOW: an automatic framework for high-throughput materials discovery, Comput. Mater. Sci. 58, 218-226 (2012). [3] K. Yang, C. Oses, and S. Curtarolo, Modeling off-stoichiometry materials with a high-throughput ab-initio approach, Chem. Mater. 28, 6484-6492 (2016). [4] P. Sarker, T. Harrington, C. Toher, K. Vecchio, and S. Curtarolo, First principles materials design using a spectral descriptor for entropy forming ability, in preparation (2017)

Modelling and synthesis of high-entropy refractory carbides, nitrides and carbonitrides

It has been well demonstrated that, through entropic stabilization, many equiatomic multicomponent metallic compositions will form single-phase, complex solid solutions, often called high-entropy alloys. It is known for metallic systems that one can take advantage of the inherent favorable properties of these materials, including increased thermal stability and solid solution strengthening. In order to extend the field of high-entropy alloys into the ultra-high temperature realm, we investigate novel equiatomic, hexanery (5-metal + anion), high-entropy refractory carbides, nitrides, and carbonitrides of group IV, V, and VI transition metals via modeling and experimental synthesis routes. The CALPHAD technique enabled rapid screening of a vast number of material systems to find likely candidates for formation of truly single-phase high-entropy ultra-high temperature ceramics (UHTCs). Compositions that exhibited broad, single-phase solubility across a large temperature region were selected, making processing possible at reasonable temperatures (≤2500°C). For further screening of compositions, a novel, first-principles materials design method was developed. The theory follows that for low temperature single-phase formation, the different configurations should have similar energies to increase the number of thermodynamically accessible states. A partial occupation method was implemented within AFLOW to automate the generation and calculation of the different configurations. The energy distributions were then used to construct a descriptor to predict the formation of high-entropy materials. Following model predictions, bulk samples were synthesized using a combination of high-energy ball milling (HEBM), spark plasma sintering (SPS) at 2200°C, and hot press (HP) annealing at 2500°C. Phase determination was done via x-ray diffraction techniques as well as TEM microscopy, while chemistry was evaluated via energy dispersive x-ray spectroscopy and STEM-EDS. Many of the carbide compositions, including (Hf0.2Nb0.2Ta0.2Ti0.2Zr0.2)C, (Hf0.2Nb0.2Ta0.2Ti0.2V0.2)C, (Hf0.2Nb0.2Ta0.2Ti0.2W0.2)C, and (Nb0.2Ta0.2Ti0.2V0.2W0.2)C demonstrated virtually single-phase, solid-solution compounds and were sintered to greater than 95% theoretical density. Figure 1 shows the experimental X-ray diffraction patterns for a sample of composition (Hf0.2Nb0.2Ta0.2Ti0.2V0.2)C following each processing step. The material progresses into the desired single cubic NaCl structure following complete processing. Work on single-phase determination in nitride and carbonitride systems is ongoing. This work demonstrates the extension of entropic-stabilization principles into refractory interstitial ceramics and development of new classes of high-entropy ceramic materials for high-temperature applications Please click Additional Files below to see the full abstract

Modelling and synthesis of high-entropy refractory carbides

Bulk samples of equiatomic, hexanery (5-metal), high-entropy refractory carbides were fabricated using a combination of high-energy ball milling (HEBM), spark plasma sintering (SPS), and hot pressing (HP) annealing. To select candidate composition that are likely to form single phase high-entropy materials at lower processing temperatures (\u3c2500°C), a novel, first-principles materials design method was developed. The theory follows that for low temperature single phase formation, the different configurations should have similar energies to increase the number of thermodynamically accessible states. A partial occupation method was implemented within AFLOW to automate the generation and calculation of the different configurations. The energy distributions were then used to construct a descriptor of Entropy Forming Ability (EFA) to predict the formation of high-entropy materials. CALPHAD results were found to agree with the configuration energy range descriptor for each composition, and these carbides exhibited broad, single-phase solubility across each system, making processing possible at reasonable temperatures. Many of the complex carbide compositions, including (Hf0.2Nb0.2Ta0.2Ti0.2Zr0.2)C, (Hf0.2Nb0.2Ta0.2Ti0.2V0.2)C, (Hf0.2Nb0.2Ta0.2Ti0.2W0.2)C, and (Nb0.2Ta0.2Ti0.2V0.2W0.2)C demonstrated virtually single-phase, solid-solution compounds with the NaCl crystal structure as determined by x-ray diffraction (XRD) and energy dispersive x-ray spectroscopy (EDS), while some compositions, including (Hf0.2Mo 0.2Ta0.2W0.2Zr0.2)C and (Hf0.2Mo0.2V0.2W0.2Zr0.2)C, exhibited multiple phases. Results were found to be in good agreement with the ab initio based formulation of entropic stability, where the compositions with the highest EFA values were found to form a single rocksalt structure and compositions with the lower EFA values were found to exhibit multiple phases. Further, among the systems that were found to form single phase materials at 2500°C, artificial segregation was introduced via lower processing temperatures. In these artificially segregated samples, the extent of mixing was analyzed via peak broadening in XRD according to the formulation of Williamson and Hall [1] and compositional mapping in EDS. Results of artificially segregated samples provide continued support for the viability of the EFA formulation, where broadening was found to be more pronounced (i.e. more chemical segregation) in samples that were determined to have a lower EFA value. This work demonstrates the extension of entropic-stabilization into refractory interstitial carbides, paving the way for development of an entirely new class of UHTCs. This work is supported by the U.S. Office of Naval Research MURI program (Grant No. N00014-15- 1-2863). [1] G.. Williamson, W.. Hall, X-ray line broadening from filed aluminium and wolfram, Acta Metall. 1 (1953) 22–31. doi:10.1016/0001-6160(53)90006-6

Fabrication of high-entropy nitrides and carbonitrides

In high-entropy alloys, the use of multiple principle alloying elements is known to entropically stabilize the material. Refractory nitrides and carbides of transition metals are widely known for their ultra high-temperature stability and their high hardness, properties that make them valuable materials for extreme environments, such as coating the exterior of hypersonic flight vehicles and the interior of nuclear reactors. By creating entropy-stabilized complex solid solutions of nitrides and carbides, one can take advantage of the inherent favorable properties of these materials, as well as increased thermal stability and solid solution strengthening. Five-metal systems are chosen using first-principles calculations to describe the energetic distribution of possible atomic configurations, in order to identify systems that are likely to form an entropy-stabilized solid solution. Bulk samples of equiatomic, hexanery (5-metal), high-entropy refractory nitrides and carbonitrides were then fabricated to demonstrate this concept, by using a combination of high-energy ball milling, spark plasma sintering, and hot pressing. The uniformity of the microstructures is characterized, and single-phase solid solutions are achieved, thus demonstrating the ability to entropically stabilize multi-component random mixtures of refractory carbides and nitrides. This work is supported by the U.S. Office of Naval Research MURI program (Grant No. N00014-15- 1-2863

High-entropy metal diborides: a new class of ultra-high temperature ceramics

Several equimolar, five-component, metal diborides were fabricated via high-energy ball milling and spark plasma sintering [Scientific Reports 6:37946 (2016)] or conventional pressure-less sintering. Most compositions synthesized, e.g., (Hf0.2Zr0.2Ta0.2Nb0.2Ti0.2)B2, (Hf0.2Zr0.2Ta0.2Mo0.2Ti0.2)B2 and several others, processed single solid-solution phases of the hexagonal AlB2 structure, while a few other compositions yielded two or more boride phases. These materials represent a new type of ultra-high temperature ceramic (UHTC) as well as a new class of high-entropy materials that possess a non-cubic (hexagonal) and layered (quasi-2D) crystal structure (Fig. 1). Please click Additional Files below to see the full abstract

Measurements and simulations of the phonon thermal conductivity of entropy stabilized alloys

The phonon thermal conductivity of solids is intimately related to any changes in atomic scale periodicity. As a classic example, the phonon thermal conductivity of alloys can be greatly reduces as compared to that of the corresponding non-alloy parent materials. However, the improved mechanical properties and environmental stability of alloyed materials makes these multi-atom solids ideal for a wide variety of applications. In this sense, entropy stabilized oxides and high entropy diborides are promising new materials that have potential to withstand extreme environments consisting of high temperatures and pressures. In these novel materials, thermal characterization is essential for understanding and predicting performance at elevated temperatures, as the presence of multi atomic species (5+ different atoms) in these solid solutions could lead to drastically modified phonon scattering rates and thermal conductivities. In this talk, we present recent measurements and molecular dynamics simulations on multiple atom alloys, including entropy stabilized oxides and high entropy diborides. We use time-domain thermoreflectance (TDTR), and optical pump-probe technique, to measure the thermal conductivity of these various systems. We also demonstrate the ability to extend TDTR measurements to temperatures above 1000 deg. C. The TDTR measurements show drastic reductions in the thermal conductivity of these crystalline solid solution materials, approaching values of the amorphous phases. These reductions in thermal conductivity can not be explained by phonon-mass scattering alone. Thus, to investigate the nature of the reduction in thermal conductivity of these multi-atom solid solutions, we turn to classical molecular dynamics simulations. In agreement with the Klemens’ perturbation theory, the thermal conductivity reduction due to mass scattering alone is found to reach a critical point, whereby adding more impurity atoms in the solid solution does not reduce the thermal conductivity. A further decrease in thermal conductivity requires a change in local strain-field, which together with mass defect scattering can lead to ultralow thermal conductivities in solid solutions, which surpasses the theoretical minimum limit of the corresponding amorphous phases. These simulations qualitatively agree well with our experimental measurements, and add insight into the nature of phonon scattering in entropy stabilized materials. This work is supported by the U.S. Office of Naval Research MURI program (grant No. N00014-15-1-2863)

Phonon scattering mechanisms contributing to the low thermal conductivities of entropy stabilized oxides and high entropy carbides

The phonon thermal conductivity of solids is intimately related to any changes in atomic scale periodicity. As a classic example, the phonon thermal conductivity of alloys can be greatly reduced as compared to that of the corresponding non-alloy parent materials. However, the improved mechanical properties and environmental stability of alloyed materials makes these multi-atom solids ideal for a wide variety of applications. In this sense, entropy stabilized oxides and high entropy carbides are promising new materials that have potential to withstand extreme environments consisting of high temperatures and pressures. In these novel materials, thermal characterization is essential for understanding and predicting performance at elevated temperatures, as the presence of multi atomic species (5+ different atoms) in these solid solutions could lead to drastically modified phonon scattering rates and thermal conductivities. In this talk, we present recent measurements and molecular dynamics simulations on multiple atom alloys, including entropy stabilized oxides and high entropy diborides. We use time-domain thermoreflectance (TDTR), and optical pump-probe technique, to measure the thermal conductivity of these various systems. We also demonstrate the ability to extend TDTR measurements to temperatures above 1000 deg. C. The TDTR measurements show drastic reductions in the thermal conductivity of these crystalline solid solution materials, approaching values of the amorphous phases. These reductions in thermal conductivity can not be explained by phonon-mass scattering alone. Thus, to investigate the nature of the reduction in thermal conductivity of these multi-atom solid solutions, we turn to classical molecular dynamics simulations. In agreement with the Klemens’ perturbation theory, the thermal conductivity reduction due to mass scattering alone is found to reach a critical point, whereby adding more impurity atoms in the solid solution does not reduce the thermal conductivity. A further decrease in thermal conductivity requires a change in local strain-field, which together with mass defect scattering can lead to ultralow thermal conductivities in solid solutions, which surpasses the theoretical minimum limit of the corresponding amorphous phases. These simulations qualitatively agree well with our experimental measurements, and add insight into the nature of phonon scattering in entropy stabilized materials. This work is supported by the U.S. Office of Naval Research MURI program (grant No. N00014-15-1-2863

Mapping local patterns of childhood overweight and wasting in low- and middle-income countries between 2000 and 2017

A double burden of malnutrition occurs when individuals, household members or communities experience both undernutrition and overweight. Here, we show geospatial estimates of overweight and wasting prevalence among children under 5 years of age in 105 low- and middle-income countries (LMICs) from 2000 to 2017 and aggregate these to policy-relevant administrative units. Wasting decreased overall across LMICs between 2000 and 2017, from 8.4% (62.3 (55.1–70.8) million) to 6.4% (58.3 (47.6–70.7) million), but is predicted to remain above the World Health Organization’s Global Nutrition Target of <5% in over half of LMICs by 2025. Prevalence of overweight increased from 5.2% (30 (22.8–38.5) million) in 2000 to 6.0% (55.5 (44.8–67.9) million) children aged under 5 years in 2017. Areas most affected by double burden of malnutrition were located in Indonesia, Thailand, southeastern China, Botswana, Cameroon and central Nigeria. Our estimates provide a new perspective to researchers, policy makers and public health agencies in their efforts to address this global childhood syndemic